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On pattern entropy of weak model sets

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arxiv 1412.6307 v4 pith:KH4HBPW7 submitted 2014-12-19 math.CO math-phmath.DSmath.MP

Christian Huck , Christoph Richard This is my paper · ORCID
classification math.COmath-phmath.DSmath.MP
keywords setsmodelentropypatternweakarisingboundboundary
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We study point sets arising from cut-and-project constructions. An important class is weak model sets, which include squarefree numbers and visible lattice points. For such model sets, we give a non-trivial upper bound on their pattern entropy in terms of the volume of the window boundary in internal space. This proves a conjecture by R.V. Moody.

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  1. Pure point measures with sparse support and sparse Fourier--Bohr support

    math.MG 2019-08 accept novelty 7.0 of 10

    Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.

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